scholarly journals Heat and Mass Transfer in the Boundary Layer of Unsteady Viscous Nanofluid along a Vertical Stretching Sheet

2014 ◽  
Vol 2014 ◽  
pp. 1-17 ◽  
Author(s):  
Eshetu Haile ◽  
B. Shankar
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Mass Transfer ◽  
Differential Equations ◽  
Heat And Mass Transfer ◽  
Stretching Sheet ◽  
Skin Friction Coefficient ◽  
Similarity Transformations ◽  
Keller Box Method ◽  
Layer Flow

Heat and mass transfer in the boundary-layer flow of unsteady viscous nanofluid along a vertical stretching sheet in the presence of magnetic field, thermal radiation, heat generation, and chemical reaction are presented in this paper. The sheet is situated in the xz-plane and y is normal to the surface directing towards the positive y-axis. The sheet is continuously stretching in the positive x-axis and the external magnetic field is applied to the system parallel to the positive y-axis. With the help of similarity transformations, the partial differential equations are transformed into a couple of nonlinear ordinary differential equations. The new problem is then solved numerically by a finite-difference scheme known as the Keller-box method. Effects of the necessary parameters in the flow field are explicitly studied and briefly explained graphically and in tabular form. For the selected values of the pertinent parameters appearing in the governing equations, numerical results of velocity, temperature, concentration, skin friction coefficient, Nusselt number, and Sherwood number are obtained. The results are compared to the works of others (from previously published journals) and they are found in excellent agreement.

g-Jitter Induced Mixed Convection Flow of Heat and Mass Transfer Past an Inclined Stretching Sheet

2014 ◽  
Vol 71 (1) ◽  
Author(s):  
Noraihan Afiqah Rawi ◽  
Abdul Rahman Mohd Kasim ◽  
Mukheta Isa ◽  
Sharidan Shafie
Keyword(s):  
Mass Transfer ◽  
Differential Equations ◽  
Mixed Convection ◽  
Heat And Mass Transfer ◽  
Stretching Sheet ◽  
Convection Flow ◽  
Convection Boundary Layer ◽  
Keller Box Method ◽  
Unsteady Mixed Convection ◽  
Layer Flow

This paper studies unsteady mixed convection boundary layer flow of heat and mass transfer past an inclined stretching sheet associated with the effect of periodical gravity modulation or g-jitter. The temperature and concentration are assumed to vary linearly with x, where x is the distance along the plate. The governing partial differential equations are transformed to a set of coupled ordinary differential equations using non-similarity transformation and solved numerically by Keller-box method. Numerical results for velocity, temperature and concentration profiles as well as skin friction, Nusselt number and Sherwood number are presented and analyzed for different values of inclination angle parameter.

scholarly journals Heat and Mass Transfer in Unsteady Boundary Layer Flow of Williamson Nanofluids

2020 ◽  
Vol 2020 ◽  
pp. 1-13 ◽  
Author(s):  
Tesfaye Kebede ◽  
Eshetu Haile ◽  
Gurju Awgichew ◽  
Tadesse Walelign
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Mass Transfer ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Thermal Radiation ◽  
Heat And Mass Transfer ◽  
Chemical Reaction ◽  
Stretching Sheet ◽  
Analytic Approximation

In this paper, analytic approximation to the heat and mass transfer characteristics of a two-dimensional time-dependent flow of Williamson nanofluids over a permeable stretching sheet embedded in a porous medium has been presented by considering the effects of magnetic field, thermal radiation, and chemical reaction. The governing partial differential equations along with the boundary conditions were reduced to dimensionless forms by using suitable similarity transformation. The resulting system of ordinary differential equations with the corresponding boundary conditions was solved via the homotopy analysis method. The results of the study show that velocity, temperature, and concentration boundary layer thicknesses generally decrease as we move away from the surface of the stretching sheet and the Williamson parameter was found to retard the velocity but it enhances the temperature and concentration profiles near the surface. It was also found that increasing magnetic field strength, thermal radiation, or rate of chemical reaction speeds up the mass transfer but slows down the heat transfer rates in the boundary layer. The results of this study were compared with some previously published works under some restrictions, and they are found in excellent agreement.

Two-Phase Flow of Fluid-Particle Interaction over a Stretching Sheet in the Presence of Magnetic Field

2019 ◽  
Vol 20 (6) ◽  
pp. 651-659
Author(s):  
J. Hasnain ◽  
Z. Abbas ◽  
M. Sajid
Keyword(s):  
Differential Equations ◽  
Stretching Sheet ◽  
Perturbation Technique ◽  
Particle Interaction ◽  
Skin Friction Coefficient ◽  
Second Grade ◽  
Two Phase ◽  
Similarity Transformations ◽  
Keller Box Method ◽  
Layer Flow

AbstractThis article presents a theoretical study of magnetohydrodynamic boundary layer flow of a dusty viscoelastic fluid over a porous stretching sheet. The basic steady equations of the viscoelastic second grade fluid and dust phases are in the form of partial differential equations. A set of coupled nonlinear ordinary differential equations is obtained by using suitable similarity transformations. The approximate first order solutions of the resulting equations are obtained using the perturbation technique. The results are also verified with the well-known finite difference technique known as Keller box method. The physical insight of the involved parameters on the velocity of both fluid and dust phases and the skin-friction coefficient is shown through graphs and tables and discussed in detail. The study shows that an increased effective viscosity increases the velocity of both fluid and particle phase.

scholarly journals Viscous Dissipation and Suction characteristics of Heat and Mass Transfer past a Stretching Sheet.

2021 ◽  
Vol 12 (1S) ◽  
pp. 623-630
Author(s):  
AlfunsaPrathiba, Et. al.
Keyword(s):  
Mass Transfer ◽  
Differential Equations ◽  
Heat And Mass Transfer ◽  
Viscous Dissipation ◽  
Schmidt Number ◽  
Stretching Sheet ◽  
Mhd Flow ◽  
Skin Friction Coefficient ◽  
Linear Ordinary Differential Equations ◽  
Similarity Transformations

in this paper, we analyzed the effect of a suction and Soret number on heat and mass transfer Magneto Hydrodynamics (MHD) flow past an exponentially stretching sheet with the heat source/sink. Appropriate similarity transformations were employed to convert the governing partial differential equations to a set of highly non-linear ordinary differential equations, which was then solved numerically by Runga kutta sixth order method together with shooting technique. The Numerical results are obtained for the skin friction coefficient, Nusselt and Sherwood numbers for selected values of the governing parameters, such as the suction, magnetic field parameter  , viscous dissipation parameter  , heat generation parameter  , Schmidt number  , and the chemical reaction rate parameter  . Besides, it is obtained that the concentration profile decreases with an increment of the Schmidt number. A comparison was made with a previous study available in the literature and we found that it is in a good agreement.

scholarly journals Inclusion of Viscous Dissipation on the Boundary Layer Flow of Cu-TiO2 Hybrid Nanofluid over Stretching/Shrinking Sheet

2021 ◽  
Vol 88 (2) ◽  
pp. 64-79
Author(s):  
Yap Bing Kho ◽  
Rahimah Jusoh ◽  
Mohd Zuki Salleh ◽  
Muhammad Khairul Anuar Mohamed ◽  
Zulkhibri Ismail ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Viscous Dissipation ◽  
Boundary Layer Flow ◽  
Skin Friction Coefficient ◽  
Shrinking Sheet ◽  
Hybrid Nanofluid ◽  
Suction Parameter ◽  
Similarity Transformations ◽  
Layer Flow

The effects of viscous dissipation on the boundary layer flow of hybrid nanofluids have been investigated. This study presents the mathematical modelling of steady two dimensional boundary layer flow of Cu-TiO2 hybrid nanofluid. In this research, the surface of the model is stretched and shrunk at the specific values of stretching/shrinking parameter. The governing partial differential equations of the hybrid nanofluid are reduced to the ordinary differential equations with the employment of the appropriate similarity transformations. Then, Matlab software is used to generate the numerical and graphical results by implementing the bvp4c function. Subsequently, dual solutions are acquired through the exact guessing values. It is observed that the second solution adhere to less stableness than first solution after performing the stability analysis test. The existence of viscous dissipation in this model is dramatically brought down the rate of heat transfer. Besides, the effects of the suction and nanoparticles concentration also have been highlighted. An increment in the suction parameter enhances the magnitude of the reduced skin friction coefficient while the augmentation of concentration of copper and titanium oxide nanoparticles show different modes.

scholarly journals A boundary layer flow analysis of a magnetohydrodynamic fluid over a shrinking sheet

2019 ◽  
Vol 11 (3) ◽  
pp. 168781401983506 ◽  
Author(s):  
Cheng-Hsing Hsu ◽  
Te-Hui Tsai ◽  
Ching-Chuan Chang ◽  
Wen-Han Huang
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Differential Equations ◽  
Boundary Layer Flow ◽  
Flow Analysis ◽  
Shear Thickening ◽  
Transformation Method ◽  
Skin Friction Coefficient ◽  
Shrinking Sheet ◽  
Layer Flow

A steady-state boundary layer flow analysis of a non-Newtonian magnetic fluid over a shrinking sheet was studied. The boundary layer thickness and the velocity distribution in the layer were studied under the conditions of a uniform magnetic field normal to the shrinking sheet and/or a vertical uniform mass suction across the sheet. The similarity transformation method was used to transform the governing partial differential equations to ordinary differential equations. The shooting method with Newton’s algorithm and Runge–Kutta integration method were used to obtain the solutions of the equations. The results showed that the variation of the flow velocity profiles in the boundary layer was significant, the thickness of the boundary layer was thinner, and the skin friction coefficient was bigger for either shear thinning or shear thickening magnetic fluids under the conditions of a stronger magnetic field or a larger mass suction effect.

scholarly journals MHD Heat and Mass Transfer Forced Convection Flow along a Vertical Stretching Sheet with Heat Generation and Radiation

1970 ◽  
Vol 46 (2) ◽  
pp. 169-176
Author(s):  
MA Samad ◽  
S Ahmed
Keyword(s):  
Magnetic Field ◽  
Mass Transfer ◽  
Differential Equations ◽  
Heat And Mass Transfer ◽  
Forced Convection ◽  
Heat Generation ◽  
Stretching Sheet ◽  
Convection Flow ◽  
Concentration Profiles ◽  
Forced Convection Flow

The present study comprises of steady two dimensional magnetohydrodynamic heat and mass transfer forced convection flow along a vertical stretching sheet in the presence of magnetic field with radiation. The nonlinear partial differential equations governing the flow field occurring in the problem have been transformed to dimensionless nonlinear ordinary differential equations by introducing suitably selected similarity variables. The ensuing equations are simultaneously solved by applying Nachtsheim-Swigert shooting iteration technique with sixth order Runge-Kutta integration scheme. The results in the form of velocity, temperature and concentration profiles are then displayed graphically. The corresponding skin-friction coefficient, Nusselt number and Sherwood number are displayed graphically and also in tabular form as well. Several important parameters such as the prandtl number (Pr), radiation parameter (N), magnetic field parameter (M), heat source parameter (Q), schmidt number (Sc), suction parameter (fw ) and eckert number (Ec) are confronted. The effects of these parameters on the velocity, temperature and concentration profiles are investigated. Key Words: MHD; Forced convection; Stretching sheet; Radiation; Heat generation. DOI: http://dx.doi.org/10.3329/bjsir.v46i2.8183 Bangladesh J. Sci. Ind. Res. 46(2), 169-176, 2011

Soret and dufour effects on MHD mixed convection heat and mass transfer in a micropolar fluid

2013 ◽  
Vol 3 (4) ◽  
Author(s):  
Darbhasayanam Srinivasacharya ◽  
Mendu Upendar
Keyword(s):  
Mass Transfer ◽  
Differential Equations ◽  
Mixed Convection ◽  
Heat And Mass Transfer ◽  
Micropolar Fluid ◽  
Nonlinear Partial Differential Equations ◽  
Skin Friction Coefficient ◽  
Soret And Dufour Effects ◽  
Similarity Transformations ◽  
Special Cases

AbstractThis paper analyzes the flow, heat and mass transfer characteristics of the mixed convection on a vertical plate in a micropolar fluid in the presence of Soret and Dufour effects. A uniform magnetic field of magnitude is applied normal to the plate. The governing nonlinear partial differential equations are transformed into a system of coupled nonlinear ordinary differential equations using similarity transformations and then solved numerically using the Keller-box method. The numerical results are compared and found to be in good agreement with previously published results as special cases of the present investigation. The rate of heat and mass transfer at the plate are presented graphically for various values of coupling number, magnetic parameter, Prandtl number, Schmidt number, Dufour and Soret numbers. In addition, the skin-friction coefficient, the wall couple stress are shown in a tabular form.

scholarly journals Multiple Slip Effects on MHD Unsteady Flow Heat and Mass Transfer Impinging on Permeable Stretching Sheet with Radiation

2019 ◽  
Vol 2019 ◽  
pp. 1-11 ◽  
Author(s):  
Fazle Mabood ◽  
Stanford Shateyi
Keyword(s):  
Mass Transfer ◽  
Differential Equations ◽  
Unsteady Flow ◽  
Heat And Mass Transfer ◽  
Stretching Sheet ◽  
Soret Effect ◽  
Skin Friction Coefficient ◽  
Multiple Slip ◽  
Slip Effects ◽  
Flow Heat

This paper reports multiple slip effects on MHD unsteady flow heat and mass transfer over a stretching sheet with Soret effect; suction/injection and thermal radiation are numerically analyzed. We consider a time-dependent applied magnetic field and stretching sheet which moves with nonuniform velocity. Suitable similarity variables are used to transform governing partial differential equations into a system of coupled nonlinear ordinary differential equations. The transformed equations are then solved numerically by applying an implicit finite difference method with quasi-linearization technique. The influences of the various parameters on the velocity temperature and concentration profiles as well as on the skin friction coefficient and Sherwood and Nusselt numbers are discussed by the aid of graphs and tables.

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